diff --git a/modules/dnn/src/onnx/onnx_importer.cpp b/modules/dnn/src/onnx/onnx_importer.cpp
index 79386e6615..47b5aff674 100644
--- a/modules/dnn/src/onnx/onnx_importer.cpp
+++ b/modules/dnn/src/onnx/onnx_importer.cpp
@@ -496,6 +496,7 @@ void ONNXImporter::populateNet(Net dstNet)
                 runLayer(layerParams, inputs, sliced);
                 CV_Assert(sliced.size() == 1);
                 constBlobs.insert(std::make_pair(layerParams.name, sliced[0]));
+                outShapes[layerParams.name] = shape(sliced[0]);
                 continue;
             }
         }
@@ -630,6 +631,8 @@ void ONNXImporter::populateNet(Net dstNet)
             Mat Wx = getBlob(node_proto, constBlobs, 1);
             Mat Wh = getBlob(node_proto, constBlobs, 2);
             Mat b = getBlob(node_proto, constBlobs, 3);
+            CV_CheckEQ(countNonZero(getBlob(node_proto, constBlobs, 5)), 0, "Unsupported non zero initial_h");
+            CV_CheckEQ(countNonZero(getBlob(node_proto, constBlobs, 6)), 0, "Unsupported non zero initial_c");
             b = b.reshape(1, b.size[0]);
 
             const int numHidden = lstmParams.get<int>("hidden_size");
@@ -1007,6 +1010,16 @@ void ONNXImporter::populateNet(Net dstNet)
             }
             else
                 layerParams.type = "Identity";
+
+            if (constBlobs.find(node_proto.input(0)) != constBlobs.end())
+            {
+                Mat inp = getBlob(node_proto, constBlobs, 0);
+                Mat out = inp.reshape(1, outShape);
+                out.dims = outShape.size();  // to workaround dims == 1
+                constBlobs.insert(std::make_pair(layerParams.name, out));
+                outShapes[layerParams.name] = shape(out);
+                continue;
+            }
         }
         else if (layer_type == "Flatten")
         {
@@ -1136,15 +1149,6 @@ void ONNXImporter::populateNet(Net dstNet)
             else
                 layerParams.type = "Identity";
         }
-        else if (layer_type == "ConstantFill" || layer_type == "ConstantOfShape")
-        {
-            CV_Assert_N(node_proto.input_size());
-            MatShape inpShape = getBlob(node_proto, constBlobs, 0);
-            float value = layerParams.get("value", 0);
-            Mat fill(inpShape.size(), &inpShape[0], CV_32F, Scalar(value));
-            constBlobs.insert(std::make_pair(layerParams.name, fill));
-            continue;
-        }
         else if (layer_type == "ConstantOfShape" || layer_type == "ConstantFill")
         {
             float fill_value;
diff --git a/modules/dnn/test/test_onnx_importer.cpp b/modules/dnn/test/test_onnx_importer.cpp
index f741319959..6932e83a4e 100644
--- a/modules/dnn/test/test_onnx_importer.cpp
+++ b/modules/dnn/test/test_onnx_importer.cpp
@@ -405,6 +405,8 @@ TEST_P(Test_ONNX_layers, Reshape)
 
 TEST_P(Test_ONNX_layers, Squeeze)
 {
+    if (backend == DNN_BACKEND_INFERENCE_ENGINE_NN_BUILDER_2019 && target == DNN_TARGET_MYRIAD)
+        applyTestTag(CV_TEST_TAG_DNN_SKIP_IE_MYRIAD, CV_TEST_TAG_DNN_SKIP_IE_NN_BUILDER);
     testONNXModels("squeeze");
 }
 
@@ -453,12 +455,12 @@ TEST_P(Test_ONNX_layers, Split_EltwiseMax)
 
 TEST_P(Test_ONNX_layers, LSTM)
 {
-    testONNXModels("lstm");
+    testONNXModels("lstm", npy, 0, 0, false, false);
 }
 
 TEST_P(Test_ONNX_layers, LSTM_bidirectional)
 {
-    testONNXModels("lstm_bidirectional");
+    testONNXModels("lstm_bidirectional", npy, 0, 0, false, false);
 }
 
 INSTANTIATE_TEST_CASE_P(/*nothing*/, Test_ONNX_layers, dnnBackendsAndTargets());